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A certain marathon had 20,000 entrants, 52% of which were female and 3
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26 Jan 2017, 09:28

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55% (hard)

Question Stats:

63%(02:42) correct 37%(02:35) wrong based on 158 sessions

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A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

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Re: A certain marathon had 20,000 entrants, 52% of which were female and 3
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26 Jan 2017, 11:06

Bunuel wrote:

A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A certain marathon had 20,000 entrants, 52% of which were female and 3
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25 Aug 2017, 22:53

2

Bunuel wrote:

A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A. 72B. 720C. 3,120D. 8,000E. 8,880

the answer is in attached image.calculated through the easiest possible method!hope it helps!

Re: A certain marathon had 20,000 entrants, 52% of which were female and 3
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25 Aug 2017, 23:16

Bunuel wrote:

A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A. 72B. 720C. 3,120D. 8,000E. 8,880

Another approach - Draw a Tree Structure for these kind of questions

As is clear from the tree structure below -No of amateur males \(= 0.036*20000 = 720\)

Re: A certain marathon had 20,000 entrants, 52% of which were female and 3
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19 Jul 2018, 11:44

Bunuel wrote:

A certain marathon had 20,000 entrants, 52% of which were female and 30% of these female entrants were professional runners. If 60% of the entrants were professional, how many of the runners in the marathon were amateur male runners?

A. 72B. 720C. 3,120D. 8,000E. 8,880

Since 52% of the 20,000 entrants were female, 0.52 x 20,000 = 10,400 were female and hence 20,000 - 10,400 = 9,600 were male. Since 30% of the female entrants were professional runners, 0.3 x 10,400 = 3,120 females were professional runners and hence 10,400 - 3,120 = 7,280 females were amateur runners.

Since 60% of the entrants were professional runners, 0.6 x 20,000 = 12,000 were professional runners and hence 20,000 - 12,000 = 8,000 were amateur runners. Since there are 7,280 female amateur runners, there are 8,000 - 7,280 = 720 male amateur runners.